VIRUS ENABLED 3D NANO-ARRAY ELECTRODES FOR INTEGRATED LI/NA-ION MICROBATTERIES

Multilayers of functional materials (carbon/electrode/nickel) were hierarchically architectured over tobacco mosaic virus (TMV) templates that were genetically modified to self-assemble in a vertical manner on current-collectors for battery applications. The spaces formed between individual rods effectively accommodated the volume expansion and contraction of electrodes during charge/discharge, while surface carbon coating engineered over these nanorods further enhance the electronic conductivity. The microbattery based on self aligned nanoforests with precise arrangement of various auxiliary material layers including a central nanometric metal core as direct electronic pathway to current collector, can deliver high energy density and stable cycling stability. C/LiFePO4/Ni/TMV nanoforest cathodes for Li-ion batteries and C/Sn/Ni/TMV nanoforest anodes for Na-ion batteries were assembled using physical sputtering deposition. Both 3D nanoforest electrodes show exceptional cycling stability and rate capability

Incompressible Limit of a Compressible Liquid Crystals System

This article is devoted to the study of the so-called incompressible limit for solutions of the compressible liquid crystals system. We consider the problem in the whole space $\mathbb{R}^{\mathbb{N}}$ and a bounded domain of $\mathbb{R}^{\mathbb{N}}$ with Dirichlet boundary conditions. Here the number of dimension $\mathbb{N}=2$ or 3

The Environmental Impact of Plastic Waste

The pollution caused by disposable plastic products is becoming more and more serious, and “plastic limit” has become a global consensus. This article mainly discusses the pollution problem from the following aspects: Integrate all relevant important indicators to establish a multiple regression model of the maximum amount of disposable plastic waste to estimate the maximum amount of disposable waste in the future without causing further damage to the environment; Establish an environmental safety level evaluation model and analyze the impact of plastic waste on environmental safety; Try to set the lowest level target that can be achieved by global waste at this stage, and conduct correlation analysis on the impact of humans, enterprises, and the environment; Select several countries based on their comprehensive strengths, conduct a comparative analysis of their plastic production, economic strength, and environment, and try to explore their responsibilities

Solution on strong partition of 22-balanced regular multipartite tournaments

We call a partition of a $c$-partite tournament into tournaments of order $c$ is strong if each tournament is strongly connected. The strong partition number denoted as $ST(r)$, represents the minimum integer $c'$ such that every regular $r$-balanced $c$-partite tournament has a strong partition with $c\geq c'$. Figueroa, Montellano-Ballesteros and Olsen showed the existence of $ST(r)$ for all $r\geq 2$ and proved that $5\leq ST(2)\leq 7$. In this note, we establish that $ST(2)=6$ and we also show the unique $2$-balanced $5$-partite tournament which has no strong partition.Comment: 10 pages, 6 figure

On degree power sum in PkP_k-free graphs

Let $G$ be a graph on $n$ vertices with degree sequence $(d_1,d_2......d_n)$. For a real $p \geq 1$, let $D_p(G)=\sum_{i=1}^nd_i^p$. A Tur\'an-type problem of degree power sum was initiated by Caro and Yuster \cite{caro2000degpower}: determining the function D_p(n,H) :=\max \{D_p(G): \text{G$is an$n$-vertex$H-free graph}\}. They obtained some exact values for certain graphs $H$. For a path $P_k$, they mentioned that ``a close examination of the proof of Theorem 1.2 shows that the value of $n_0(k)$ in the statement of the theorem is $O(k^2)$", namely, they could show the $n$-vertex $P_k$-free graph with maximum degree power sum is $W_{n,k-1,\lfloor \frac{k}{2} \rfloor -1} = K_{\lfloor \frac{k}{2} \rfloor -1} \vee \left((n - \lceil \frac{k}{2} \rceil)K_1 \cup K_{1+k-2\lfloor \frac{k}{2} \rfloor} \right)$ when $n \geq c k^2$ for some constant $c$. In this note, we improve their result to a linear size of $k$ by a different approach. The bound is tight up to a constant factor.Comment: 6 page

CBISI-LSTM Deep Learning Model for Short-term Cross-border Capital Flow Prediction

With the drastic fluctuation of the international financial market in recent years, the cross-border capital flow between Shanghai and Hong Kong has become increasingly active. The lack of effective and timely tracking monitoring and scientific management of cross-border capital flow in the capital market will seriously affect the overall financial security of China\u27s economy. This paper constructs the cross-border investor sentiment index CBISI based on principal component analysis and analyzes the impact of cross-border investor sentiment and cross-border capital flows by constructing the VAR model. In addition, CBISI is used as part of the input variable of LSTM to forecast the cross-border capital flow (NF). The findings of the study indicate that changes in cross-border investor sentiment will have a significant short-term impact on cross-border capital flows, and the addition of CBISI will improve the accuracy of cross-border flow estimates